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Substitute Numbers for Letters in Simple Sums

In this worksheet, students will replace letters with numbers and carry out simple questions using the four number operations. (The student will type the answer as a number and no prioritisation of calculations is required at this stage.)

Worksheet Overview

QUESTION 1 of 10

Make sure that you’ve got your thinking cap on as we are going to be number decoders!

In this activity, we are going to swap numbers for letters to solve maths problems.

Let’s take a look at this question first:

If a = 1, b = 2, c = 3 and d = 4, what is c x d?

This is called algebra, which is where numbers are replaced with letters. We need to swap the letters back into numbers to solve this problem.

If we put the numbers back in, then c x d becomes 3 x 4. We know this is 12.

The values of the letters can be different in each question.

Let’s try this question next:

If a = 7, b = 4, c = 8 and p = 3, what is a + b + c?

Let’s swap the letters back to numbers. This would be written as: 7 + 4 + 8 = 19.

Remember, when you are adding lots of numbers, you can choose the order that you add them in.

If there is a mixture of addition and subtraction, you must work it out in the order that it is written.

Let’s practise this now:

If a = 10, b = 4, c = 3 and d = 9, what is b + d - a + c?

Let’s swap the letters back to numbers. This would be written as: 4 + 9 - 10 + 3 =

Remember, we must answer this one in order.

So 4 + 9 = 13…

13 - 10 = 3…

3 + 3 = 6.

Now it’s your turn to crack the codes. Good luck number detective!

Let's continue practising converting between letters and numbers, but not we are going to explore more options than just + and -.

If A = 1, B = 2, C = 3 and D = 4, what is C x D?

Can you choose the correct number sentence from the options below?

1 x 2

3 x 4

3 + 4

4 x 1

Following on from the last step:

What is 3 x 4?

If a = 3, b = 4, c = 5 and d = 6, what is d x b?

Can you choose the correct number sentence from the options below?

6 - 4

6 + 4

6 x 4

5 x 4

Following on from the last step:

What is 6 x 4?

If a = 7, b = 5, c = 3 and d = 2, which letters have been used to make the sum 7 x 3?

Can you choose the correct number sentence from the options below?

b x c

a x c

b x a

a + c

If A = 7, B = 5, C = 3 and D = 2, what is A x C?

Can you type the answer to this question as a number?

If A = 10, B = 12, C = 7 and D = 8, which letters have been used to make the sum 10 x 12?

Can you choose the correct number sentence from the options below?

B - A

B x C

A x B

B + A

If a = 10, b = 12, c = 7 and d = 8, what is a x b?

Can you type the answer to this question as a number?

If A = 3, B = 17, C = 15 and D = 9, which letters have been used to give an answer of 27?

Can you choose the correct letter sentence from the options below?

C + D

D x A

B + D

A + B + D

If A = 3, B = 7, C = 15 and D = 9, which letters have been used to give an answer of 21?

Can you choose the correct letter sentence from the options below?

B + C

C + D

A x B

A x D

ANSWERS

Question 1

Let's continue practising converting between letters and numbers, but not we are going to explore more options than just + and -.

If A = 1, B = 2, C = 3 and D = 4, what is C x D?

Can you choose the correct number sentence from the options below?

CORRECT ANSWER

3 x 4

EDDIE SAYS

The question tells us that C = 3 and D = 4.
If we swap the letters for the numbers they represent, we find that C x D becomes 3 x 4.
Similarly to addition (+) questions, we can switch around the order of the two numbers in a multiplication sum and we will still get the same answer.

ANSWERS

Question 2

Following on from the last step:

What is 3 x 4?

CORRECT ANSWER

12

EDDIE SAYS

3 x 4 means the same as 3 groups of 4 or 4 + 4 + 4.
We can also switch the numbers around to get the same answer, so 4 x 3 or 4 groups of 3, or 3 + 3 + 3 + 3.
The answer to either 3 x 4 or 4 x 3 is 12.

ANSWERS

Question 3

If a = 3, b = 4, c = 5 and d = 6, what is d x b?

Can you choose the correct number sentence from the options below?

CORRECT ANSWER

6 x 4

EDDIE SAYS

The question tells us that d = 6 and b = 4.
If we swap the letters for the numbers they represent, we find that d x b becomes 6 x 4.
Similarly to addition (+) questions, we can switch around the order of the two numbers in a multiplication sum and we will still get the same answer.
Also, remember that the letters, and numbers associated with them, will often change in each question so you need to keep your eyes peeled!

ANSWERS

Question 4

Following on from the last step:

What is 6 x 4?

CORRECT ANSWER

24

EDDIE SAYS

6 x 4 means the same as 6 groups of 4 or 4 + 4 + 4 + 4 + 4 + 4.
We can also switch the numbers around to get the same answer, so 4 x 6 or 4 groups of 6, or 6 + 6 + 6 + 6.
The answer to either 6 x 4 or 4 x 6 is 24.

ANSWERS

Question 5

If a = 7, b = 5, c = 3 and d = 2, which letters have been used to make the sum 7 x 3?

Can you choose the correct number sentence from the options below?

CORRECT ANSWER

a x c

EDDIE SAYS

The question tells us that a = 7 and c = 3.
If we swap letters in place of the numbers which they represent, we find that 7 x 3 becomes a x c.
As the numbers in multiplication (x) sums can be switched around, c x a would also give us the same answer and be correct.

ANSWERS

Question 6

If A = 7, B = 5, C = 3 and D = 2, what is A x C?

Can you type the answer to this question as a number?

CORRECT ANSWER

21

EDDIE SAYS

The question tells us that A = 7 and C = 3.
If we swap the letters for the numbers they represent, we find that A x C becomes 7 x 3.
The answer to 7 x 3 is 21.

ANSWERS

Question 7

If A = 10, B = 12, C = 7 and D = 8, which letters have been used to make the sum 10 x 12?

Can you choose the correct number sentence from the options below?

CORRECT ANSWER

A x B

EDDIE SAYS

The question tells us that A = 10 and B = 12.
If we swap letters in place of the numbers which they represent, we find that 10 x 12 becomes A x B.
As the numbers in multiplication (x) sums can be switched around, B x A would also give us the same answer and be correct.

ANSWERS

Question 8

If a = 10, b = 12, c = 7 and d = 8, what is a x b?

Can you type the answer to this question as a number?

CORRECT ANSWER

120

EDDIE SAYS

The question tells us that a = 10 and b = 12.
If we swap the letters for the numbers they represent, we find that a x b becomes 10 x 12.
The answer to 10 x 12 is 120.

ANSWERS

Question 9

If A = 3, B = 17, C = 15 and D = 9, which letters have been used to give an answer of 27?

Can you choose the correct letter sentence from the options below?

CORRECT ANSWER

D x A

EDDIE SAYS

We need to get to an answer of 27 using a combination of the numbers given in the question.
Can you think of an calculation in your times tables which gives an answer of 27 using some of the numbers given?
After trying different combinations, we can see that 9 x 3 will give us our target of 27.
If we swap letters in place of the numbers which they represent, we find that 9 x 3 becomes D x A.
As the numbers in multiplication (x) sums can be switched around, A x D would also give us the same answer and be correct.

ANSWERS

Question 10

If A = 3, B = 7, C = 15 and D = 9, which letters have been used to give an answer of 21?

Can you choose the correct letter sentence from the options below?

CORRECT ANSWER

A x B

EDDIE SAYS

We need to get to an answer of 21 using a combination of the numbers given in the question.
Can you think of an calculation in your times tables which gives an answer of 21 using some of the numbers given?
After trying different combinations, we can see that 3 x 7 will give us our target of 21.
If we swap letters in place of the numbers which they represent, we find that 3 x 7 becomes A x B.
As the numbers in multiplication (x) sums can be switched around, B x A would also give us the same answer and be correct.

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